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The Surface Area Of A Scalene Cone As Solved By Varignon, Leibniz, And Euler, Daniel J. Curtin 2021 Northern Kentucky University

The Surface Area Of A Scalene Cone As Solved By Varignon, Leibniz, And Euler, Daniel J. Curtin

Euleriana

In a 1727 mathematical compendium, Pierre Varignon (1654-1722) published his solution to the problem of finding the surface area of a scalene (oblique) cone, one whose base is circular but whose vertex is off-center. The article after Varignon's in that publication was by Gottfried Leibniz (1646-1716), who proposed improvements and even extended the solution to a base with any curve. When Leonhard Euler (1707-1783) published on the subject [E133] in 1750, he gently pointed out an error in Leibniz's solution, which he corrected, after extending Varignon's solution in the case of circular base. Euler then used Leibniz ...


Collecting Works: A History Of The Euler Archive, Erik R. Tou, Christopher Goff, Michele Gibney 2021 University of Washington – Tacoma

Collecting Works: A History Of The Euler Archive, Erik R. Tou, Christopher Goff, Michele Gibney

Euleriana

We give a brief history of the Euler Archive, an online database of the published works of Leonhard Euler (1707-1783). Furthermore, we describe the Archive's recent move to an academic repository, and the added functionality such a move allows.


A New Look At Euler And His Contemporaries, Christopher Goff, Erik Tou 2021 University of the Pacific

A New Look At Euler And His Contemporaries, Christopher Goff, Erik Tou

Euleriana

Introducing Euleriana: Volume 1, Issue 1.


Traveling Wave Phenomena In A Nonlocal Dispersal Predator-Prey System With The Beddington-Deangelis Functional Response And Harvesting, Zhihong Zhao, Yan Li, Zhaosheng Feng 2021 The University of Texas Rio Grande Valley

Traveling Wave Phenomena In A Nonlocal Dispersal Predator-Prey System With The Beddington-Deangelis Functional Response And Harvesting, Zhihong Zhao, Yan Li, Zhaosheng Feng

Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder's fixed point theorem, we show that there exists a positive constant c∗ such that the system possesses a traveling wave solution for any given c>c∗. Moreover, the asymptotic behavior of traveling wave solution at infinity is obtained by the contracting rectangles method. The existence of traveling wave solution for c=c∗ is established by means of Corduneanu's theorem. The nonexistence ...


Fuzzy P-Value Of Hypotheses Tests With Crisp Data Using Non-Asymptotic Fuzzy Estimators, Nikos Mylonas, Basil K. Papadopoulos 2021 Democritus University of Thrace, Kimeria, Xanthi, 67100, Greece

Fuzzy P-Value Of Hypotheses Tests With Crisp Data Using Non-Asymptotic Fuzzy Estimators, Nikos Mylonas, Basil K. Papadopoulos

Journal of Stochastic Analysis

No abstract provided.


The 2020 National Snow Load Study, Brennan Bean, Marc Maguire, Yan Sun, Jadon Wagstaff, Salam Adil Al-Rubaye, Jesse Wheeler, Scout Jarman, Miranda Rogers 2021 Utah State University

The 2020 National Snow Load Study, Brennan Bean, Marc Maguire, Yan Sun, Jadon Wagstaff, Salam Adil Al-Rubaye, Jesse Wheeler, Scout Jarman, Miranda Rogers

Mathematics and Statistics Faculty Publications

The United States has a rich history of snow load studies at the state and national level. The current ASCE 7 snow loads are based on studies performed at the Cold Regions Research and Engineering Laboratory (CRREL) ca. 1980 and updated ca. 1993. The map includes large regions where a site-specific case study is required to establish the load. Many state reports attempt to address the "case-study regions" designated in the current ASCE 7 design snow load requirements. The independently developed state-specific requirements vary in approach, which can lead to discrepancies in requirements at state boundaries. In addition, there has ...


Courant Cohomology, Cartan Calculus, Connections, Curvature, Characteristic Classes, Miquel Cueca, Rajan Amit Mehta 2021 Georg-August-Universität Göttingen

Courant Cohomology, Cartan Calculus, Connections, Curvature, Characteristic Classes, Miquel Cueca, Rajan Amit Mehta

Mathematics and Statistics: Faculty Publications

We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan formula for the de Rham differential. This perspective allows us to develop the theory of Courant algebroid connections in a way that mirrors the classical theory of connections. Using a special class of connections, we construct secondary characteristic classes associated to any Courant algebroid.


Some Model Theory Of Free Groups, Christopher James Natoli 2021 The Graduate Center, City University of New York

Some Model Theory Of Free Groups, Christopher James Natoli

Dissertations, Theses, and Capstone Projects

There are two main sets of results, both pertaining to the model theory of free groups. In the first set of results, we prove that non-abelian free groups of finite rank at least 3 or of countable rank are not A-homogeneous. We then build on the proof of this result to show that two classes of groups, namely finitely generated free groups and finitely generated elementary free groups, fail to form A-Fraisse classes and that the class of non-abelian limit groups fails to form a strong A-Fraisse class.

The second main result is that if a countable group is elementarily ...


Global-In-Time Solvability And Blow-Up For A Non-Isospectral Two-Component Cubic Camassa-Holm System In A Critical Besov Space, Lei Zhang, Zhijun Qiao 2021 The University of Texas Rio Grande Valley

Global-In-Time Solvability And Blow-Up For A Non-Isospectral Two-Component Cubic Camassa-Holm System In A Critical Besov Space, Lei Zhang, Zhijun Qiao

Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we prove the global Hadamard well-posedness of strong solutions to a non-isospectral two-component cubic Camassa-Holm system in the critical Besov space B2,11/2(T). Our results show that in comparison with the well-known work for classic Camassa-Holm-type equations, the existence of global solution only relies on the L1-integrability of the variable coefficients α(t) and γ(t), but nothing to do with the shape of the initial data. The key ingredient of the proof hinges on the careful analysis of the mutual effect among two component forms, the uniform bound of approximate solutions, and several crucial ...


Math In The Time Of Covid: An Open Call For Contributions, Mark Huber, Gizem Karaali 2021 Claremont McKenna College

Math In The Time Of Covid: An Open Call For Contributions, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics invites submissions of essays, reflections, poetry, and artwork for an upcoming thematic folder tentatively titled Math in the Time of COVID and scheduled to appear in July 2021. Please send your submissions via email to the editors by May 1, 2021. Publication decisions will be made by June 15, 2021.


Special Issue Call For Papers: Ethics In Mathematics, Catherine Buell, Victor Piercey 2021 Fitchburg State University

Special Issue Call For Papers: Ethics In Mathematics, Catherine Buell, Victor Piercey

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Ethics in Mathematics. Please send your abstract submissions via email to the guest editors by September 1, 2021. Initial submission of complete manuscripts is due December 1, 2021. The issue is currently scheduled to appear in July 2022.


Once Upon A Party - An Anecdotal Investigation, Vijay Fafat 2021 Ariana Investment Management

Once Upon A Party - An Anecdotal Investigation, Vijay Fafat

Journal of Humanistic Mathematics

Mathematicians and Physicists attending let-your-hair-down parties behave exactly like their own theories. They live by their theorems, they jive by their theorems. Life imitates their craft, and we must simply observe the deep truths hiding in their party-going behavior...


Deterministic Republic, Kris H. Green 2021 St. John Fisher College

Deterministic Republic, Kris H. Green

Journal of Humanistic Mathematics

This story is an extension of the paper "Mathematics and Voter Choice" published in this same issue of the Journal of Humanistic Mathematics. It explores what elections and politics might look like from the voter perspective if some of the ideas from the paper were implemented. The story is also an attempt to highlight how mathematics and data science are done, much the way a colleague of mine refers to shows like CSI as recruiting tools that use "dramatic pipetting" in the labs to show day-to-day science in action. The story is, as you will no doubt see, heavily influenced ...


Iterations Of Emptying, Marian Christie 2021 Claremont Colleges

Iterations Of Emptying, Marian Christie

Journal of Humanistic Mathematics

Successive iterations of the Sierpinski carpet fractal are used to explore how we---our history, experiences, thoughts and memories---occupy spaces that we once inhabited.


Turing's Machine, Mike Curtis 2021 Shrewsbury U3A, UK

Turing's Machine, Mike Curtis

Journal of Humanistic Mathematics

The musings of a Turing Machine.


One Straight Line Addresses Another Traveling In The Same Direction On An Infinite Plane, Daniel W. Galef 2021 McGill University

One Straight Line Addresses Another Traveling In The Same Direction On An Infinite Plane, Daniel W. Galef

Journal of Humanistic Mathematics

No abstract provided.


Proof Theory, Stan Raatz 2021 None

Proof Theory, Stan Raatz

Journal of Humanistic Mathematics

No abstract provided.


Early Morning Mathematics Classes, Angelina Schenck 2021 University of Minnesota-Twin Cities

Early Morning Mathematics Classes, Angelina Schenck

Journal of Humanistic Mathematics

No abstract provided.


Permission To Add: Math-Teaching Limericks, Marion D. Cohen 2021 Drexel University

Permission To Add: Math-Teaching Limericks, Marion D. Cohen

Journal of Humanistic Mathematics

Throughout my years and decades of being a teacher, I have written limericks about every course I’ve taught, and sometimes courses I haven’t taught but reviewed textbooks in. Here I share several of these limericks.


Peter Hilton En Passant, Richard Delaware 2021 University of Missouri- Kansas City

Peter Hilton En Passant, Richard Delaware

Journal of Humanistic Mathematics

This is a decades-long tale of my glancing friendship with distinguished mathematician and mathematics educator Peter Hilton and his constant collaborator Jean Pedersen. Peter’s wit, compassion, and support are in full display, though in truth I knew him only “in passing.”


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